Tim Wescott <[email protected]> wrote:
> A sphere is a three dimensional figure enclosed by the locus of all
> points that are of distance r (called the radius) away from the center
> point. It has a volume of 4/3 pi r^3 and a surface area of 4 pi r^2.
(snip)

> Now hopefully I have some momentum: The four dimensional analog of a
> sphere (commonly called a hypersphere) is a four dimensional figure
> enclosed by the locus of all points that are a distance of r away from
> the center point. It contains an amount of space (not a volume,
> certainly -- hypervolume?) equal to 1/2 pi^2 r^4, and has a 'surface'
> volume of 2 pi^2 r^3.

The surface volume agrees with mathworld. The hypervolume seems
to be an easy integral, so I agree with that one, too.

-- glen